Elliptic curves over $\Q$ of conductor 12502

Results (9 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
12502.a1	12502a1	12502.a	12502a	$2$	$2$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{2} \cdot 7^{3} \cdot 19^{2} \cdot 47 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$50008$	$12$	$0$	$0.373014117$	$1$		$9$	$3360$	$0.251400$	$3733252610697/23278724$	$0.93119$	$3.06862$	$[1, -1, 0, -323, 2305]$	\(y^2+xy=x^3-x^2-323x+2305\)	2.3.0.a.1, 152.6.0.?, 658.6.0.?, 50008.12.0.?	$[(12, 1)]$
12502.a2	12502a2	12502.a	12502a	$2$	$2$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( - 2 \cdot 7^{6} \cdot 19 \cdot 47^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$50008$	$12$	$0$	$0.746028234$	$1$		$4$	$6720$	$0.597974$	$-261284780457/9875692358$	$0.93608$	$3.23133$	$[1, -1, 0, -133, 4851]$	\(y^2+xy=x^3-x^2-133x+4851\)	2.3.0.a.1, 152.6.0.?, 1316.6.0.?, 50008.12.0.?	$[(-7, 77)]$
12502.b1	12502b1	12502.b	12502b	$1$	$1$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$12502$	$2$	$0$	$1.266098061$	$1$		$2$	$1536$	$-0.345373$	$-95443993/100016$	$0.73623$	$2.05727$	$[1, 0, 1, -10, -20]$	\(y^2+xy+y=x^3-10x-20\)	12502.2.0.?	$[(5, 5)]$
12502.c1	12502c3	12502.c	12502c	$4$	$4$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( 2 \cdot 7^{4} \cdot 19^{2} \cdot 47^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.58	2B	$2632$	$48$	$0$	$1$	$1$		$0$	$18944$	$1.182959$	$25172562615580017/8459034366482$	$0.92723$	$4.00318$	$[1, -1, 1, -6106, -117385]$	\(y^2+xy+y=x^3-x^2-6106x-117385\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 2632.48.0.?	$[]$
12502.c2	12502c2	12502.c	12502c	$4$	$4$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{2} \cdot 7^{2} \cdot 19^{4} \cdot 47^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.1	2Cs	$2632$	$48$	$0$	$1$	$1$		$2$	$9472$	$0.836385$	$1719073016770257/56424301444$	$0.95895$	$3.71867$	$[1, -1, 1, -2496, 47231]$	\(y^2+xy+y=x^3-x^2-2496x+47231\)	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 1316.24.0.?, 2632.48.0.?	$[]$
12502.c3	12502c1	12502.c	12502c	$4$	$4$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{4} \cdot 7 \cdot 19^{2} \cdot 47 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.50	2B	$2632$	$48$	$0$	$1$	$1$		$3$	$4736$	$0.489811$	$1678074290715537/1900304$	$0.89842$	$3.71611$	$[1, -1, 1, -2476, 48031]$	\(y^2+xy+y=x^3-x^2-2476x+48031\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 658.6.0.?, 1316.24.0.?, $\ldots$	$[]$
12502.c4	12502c4	12502.c	12502c	$4$	$4$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( - 2 \cdot 7 \cdot 19^{8} \cdot 47 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.103	2B	$2632$	$48$	$0$	$1$	$4$	$2$	$0$	$18944$	$1.182959$	$55424004754383/11175184480978$	$1.02907$	$3.97477$	$[1, -1, 1, 794, 160407]$	\(y^2+xy+y=x^3-x^2+794x+160407\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 1316.12.0.?, 2632.48.0.?	$[]$
12502.d1	12502e1	12502.d	12502e	$1$	$1$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( - 2 \cdot 7 \cdot 19 \cdot 47 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$50008$	$2$	$0$	$1$	$1$		$0$	$624$	$-0.525698$	$16581375/12502$	$0.70087$	$1.76218$	$[1, -1, 1, 5, 1]$	\(y^2+xy+y=x^3-x^2+5x+1\)	50008.2.0.?	$[]$
12502.e1	12502d1	12502.e	12502d	$1$	$1$	\( 2 \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{4} \cdot 7^{7} \cdot 19^{4} \cdot 47 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1316$	$2$	$0$	$0.206983110$	$1$		$6$	$60928$	$1.615540$	$-143563142482697477233/80708360371856$	$0.94318$	$4.92008$	$[1, 0, 0, -109087, 13865449]$	\(y^2+xy=x^3-109087x+13865449\)	1316.2.0.?	$[(72, 2491)]$